The invention relates to the determination of not only the size distribution, but also the compressibility and thermal expansion coefficients of the particles, from the measured ultrasound attenuation frequency spectra and sound speed.
This invention deals with a particular kind of dispersed system (or colloid) that can be described as a collection of small soft particles immersed in a liquid. These particles can be either solid (latex) or liquid (emulsions). Such dispersed systems play an important role in all kind of paints, lattices, food products, paper coatings, polymer solutions, etc.
These systems have a common feature. Because of the small particle size, the total surface area of the particles is large relative to their total volume. Therefore surface related phenomena determine their behavior in various processes. This invention has particular application to dispersed systems where these surface effects are dominant, corresponding to a range of particle size up to about 10 microns. The importance of these surface effects disappears for larger particles.
The characterization of such colloids is important not only for the manufacture, but also the development of new systems with improved properties. Particle size distribution is a one of the basic notions for characterizing these dispersed systems. Several methods are known for determining particle size. Most methods are based on light, for example: light scattering; light diffraction; etc. There is a new alternative method based on ultrasound that is rapidly becoming important. This ultrasound method has a large advantage over traditional light-based techniques because it is able to characterize a concentrated system without dilution. Light-based methods usually require extreme dilution in order to make the sample sufficiently transparent for measurement. This invention deals with improvements of this ultrasound characterization technique.
There are two methods for ultrasound characterization of disperse systems: Acoustics and Electroacoustics. This invention deals only with Acoustics.
This acoustic method involves two steps. The first step is to perform an experiment on the disperse system to obtain a set of measured values for certain macroscopic properties such as temperature, pH, attenuation spectra, sound speed, etc. This invention does not deal with this step. It assumes the availability of instruments for accurate and precise measurement of the ultrasound attenuation and sound speed. One of the possible examples is described in U.S. Pat. No. 6,109,098 by Dukhin, A. S. and Goetz, P. J. xe2x80x9cMethod and device for characterizing particle size distribution and zeta potential in concentrated system by means of Acoustic and Electroacoustic Spectroscopyxe2x80x9d.
The second step is an analysis of the measured data to compute the desired microscopic properties such as particle size. Such an analysis requires three tools: a model dispersion, a prediction theory, and an analysis engine.
A xe2x80x9cmodel dispersionxe2x80x9d is an attempt to describe the real dispersion in terms of a set of model parameters including, of course, the desired microscopic characteristics. The model, in effect, makes a set of assumptions about the real world in order to simplify the complexity of the dispersion and thereby also simplify the task of developing a suitable prediction theory. For example, most particle size measuring instruments make the assumption that the particles are spherical and therefore a complete geometrical description of the particle is given by a single parameter, its diameter. Obviously such a model would not adequately describe a dispersion of carpet fibers that have a high aspect ratio and any theory based on this over-simplified model might well give incorrect results. The model dispersion may also attempt to limit the complexity of the particle size distribution by assuming that it can be described by certain conventional distribution functions, such as for example a lognormal distribution.
A xe2x80x9cprediction theoryxe2x80x9d consists of a set of equations that describes some of the measured macroscopic properties in terms of these microscopic properties of the model dispersion. For example, a prediction theory for acoustics would attempt to describe a macroscopic property such as the ultrasound attenuation in terms of such microscopic properties as the particle size distribution, volume fraction of the dispersed phase and various physical properties of the particles and liquid.
An xe2x80x9canalysis enginexe2x80x9d is essentially a set of algorithms, implemented in a computer program that calculates the desired microscopic properties from the measured macroscopic data using the knowledge contained in the prediction theory. The analysis can be thought of as the opposite or inverse of prediction. Prediction describes some of the measured macroscopic properties in terms of the model dispersion. Analysis, given only the values for some of the model parameters, attempts to calculate the remaining properties by an analysis of the measured data. There are many well-documented approaches to this analysis task.
This invention suggest a new xe2x80x9canalysis enginexe2x80x9d. The measurement part, xe2x80x9cmodel dispersionxe2x80x9d and xe2x80x9cprediction theoryxe2x80x9d are exactly the same as described in our previous invention, U.S. Pat. No. 6,109,098. The xe2x80x9canalysis enginexe2x80x9d described in this patent required a certain set of input parameters for calculating the particle size distribution from the measured attenuation spectra. In particular, for dispersions of soft particles such as latexes and emulsions, it was necessary to specify a thermal expansion coefficient and compressibility of the particle materials. In many cases this data was not available, which made it impossible to apply acoustic techniques for characterizing the particle size in these dispersions.
In this invention we suggest a means to extract this unknown data about the mechanical properties of the particles from the measured attenuation spectra and sound speed. This eliminates the need to know these mechanical properties in advance. We show that the attenuation spectra and sound speed contains sufficient information to calculate both the particle size as well as the above-mentioned mechanical properties of the particles.
The applicant describes a new xe2x80x9canalysis enginexe2x80x9d for calculating not only the particle size distribution from the measured attenuation spectra and sound speed but in addition mechanical properties such as compressibility and the thermal expansion coefficient.